a + b + c = 0
a3 + b3 + c3 = a5 + b5 + c5
demostrar
a2 + b2 + c2 = 6 / 5
Resolveremos el problema utilizando funciones simétricas ...
e1 = p1 = 0
p3 = p5
en = 0 , n > 3
donde en representan a las funciones simétricas elementales y pn a las funciones simétricas de las sumas de potencias.
Expresando las sumas de potencias en función de las funciones unitarias.
p2 = −2 e2
p3 = 3 e3
p5 = −5 e2 e3
p3 = p5
3 e3 = −5 e2 e3
e2 = − 3 / 5
∴ p2 = 6 / 5
∎
Media
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